Two pairs of shoes and four pairs of socks cost $125, and three pairs of shoes and five pairs of socks cost $182. Find the cost of a pair of socks.
$
b = shoe price
s = sock price
2 b + 4 s = 125 times 3
3 b + 5 s = 182 times 2
6 b + 12 s = 375
6 b + 10 s = 364
----------------- subtract
2 s = 11
s = $5.50
To find the cost of a pair of socks, we can set up a system of equations using the given information.
Let's assume the cost of a pair of shoes is represented by 'S', and the cost of a pair of socks is represented by 'C'.
From the first statement, we know that two pairs of shoes (2S) and four pairs of socks (4C) cost $125. This can be written as:
2S + 4C = 125 ............(1)
From the second statement, we know that three pairs of shoes (3S) and five pairs of socks (5C) cost $182. This can be written as:
3S + 5C = 182 ............(2)
Now, we can solve this system of equations to find the values of 'S' and 'C'.
Multiplying equation (1) by 3 and equation (2) by 2, we get:
6S + 12C = 375 ...........(3)
6S + 10C = 364 ...........(4)
Subtracting equation (4) from equation (3), we have:
6S + 12C - (6S + 10C) = 375 - 364
2C = 11
Dividing both sides of the equation by 2, we find:
C = 11/2
C = $5.50
Therefore, the cost of a pair of socks is $5.50.